Tag Archives: vix

Higher Interest Rates Lead To Increased Volatility – How To Prepare For A Volatile Market

Summary Again, the Fed is threatening to raise interest rates. The results of my statistical study show that increasing interest rates leads to an increase in overall market volatility. Whether liquidating or investing in an increasingly volatile market, you have several strategies that can give you an advantage. I have had several requests for statistical analyses on individual stocks, but recently I was asked to look into the correlation between interest rates and volatility. This request does not come as a surprise for two reasons. First, although Chairwoman Yellen recently passed on raising interest rates , others are stating that, regardless, we will see a rise in interest rates this year . Many are asking what will happen to the market once this happens. Second, the VIX and its associated ETF, the iPath S&P 500 VIX Short-Term Futures ETN (NYSEARCA: VXX ), are looking increasingly bumpy. This time of year tends to bring bumps in the VIX, with a dip and subsequent rally. Investors are wondering what will happen to the VIX (which can be thought of as an overall measurement of how risky the market is at the current time) if interest rates increase. An increase in interest rates could just be the catalyst to bring back market volatility. But does an increase in interest rates truly bring an increase in volatility? Though I could find a few articles online claiming this fact, I found no previous statistical analyses on the subject. Some images backing the claim of a correlation between interest rates and volatility are examples of exactly what you don’t want to rely on as an investor: curve-fitting. I’ve seen too many “analysts” run models over and over until they find a couple of curves that seem to line up. This is exactly what the following two images display: The first chart shows the T-bill yield and VIX apparently lining up in perfect accord. But there are three problems here: First, a logarithmic transform was applied to the VIX line. This changes the shape of the VIX line. I suspect this was done to make the VIX curve better resemble the yield. While logarithmic scales can be useful for looking at indexes or stocks – especially when comparing two stocks trading at drastically different ranges – logarithmic scales should not be used without reason. A proper statistical model first states that the logarithmic scale should be used and gives reason for using it. I suspect that this analyst simply found the logarithmic conversion to produce the curve he wanted, meaning he was playing with data to confirm his conclusion rather than performing a true analysis. Second, the yield was transposed two years. Again, this is likely an action with the motive of making the two curves match. If the yield was not transposed to the right, the graph would show the opposite of what the author wanted – i.e., the graph would imply that yield and the VIX have a negative correlation! It simply makes no sense to move one index two years forward in time. This is especially true when the T-bill used is only a 3-month T-bill! Is the analyst trying to say that the VIX today can predict the price of a 3-month T-bill two years from now?! The second chart is equally absurd. This time, the VIX is plotted with the 2-year and 10-year yield curve (i.e., the slope of the yield curve, measuring the difference between the yield of a 10-year bond and 2-year bond). The absurdities follow: First, this analyst does the same as the previous analyst; he moves the entire yield curve forward two years. Again, this would imply that the VIX today is predicting something precisely two years from now. This is another sign of curve-fitting. Second, the analyst inverts the yield curve. There is simply no reason to do so – unless, of course, your goal is to get a desired look to your chart so you can draw a conclusion, which is the exact definition of curve fitting. Interpreting the inverse of a function in words is a difficult task – so knowing that the VIX is correlated with the 2-year future inverse of the yield curve tells us nothing! As you have probably concluded, we need a more formal way of determining the relationship between interest rates and the VIX. In this study, I set up the following set of hypotheses and test them statistically: Set 1: H0: The VIX is uncorrelated with yield rates H1: The VIX is correlated with yield rates Set 2: H0: The VIX is uncorrelated with the yield curve H1: The VIX is correlated with the yield curve The Study As you can see, the test will be simple – no data transformations or curve-fitting. I collected the data from the VIX for each day, starting from 2004. I did the same for the bond market. Because the stock market and bond market have a few days per year in which one market is closed while the other is open, I removed such dates from the analysis. I did so to allow a one-to-one comparison for the VIX and yield each day in the market. Thus, daily movements in the VIX and movements in the bond market will be tracked. For the VIX data, I used the closing values. For the bond data, I used 2-year bonds, which is more or less the “middle ground” for bonds. For the yield curve, I used the difference between 1-month and 20-year bonds, giving the widest and most sensitive curve. If anyone has any qualms with these choices, please let me know in the comments section below and I can rerun the analysis with your chosen values (e.g., daily VIX highs vs. 20-year bonds). I used an alpha level of 0.05 as the comparison point for the p-value. Correlation tests for the hypotheses that reported p-values less than 0.05 would be considered evidence for the rejection of H0, giving strong evidence for H1. The Results The results follow: Yield Yield Curve Correlation with VIX -0.2680 0.3581 p-value for correlation depreciated dollar -> increased yield curve -> increased VIX But the yield curve is actually moderated by the supply and demand of capital. Decreases in the money supply (e.g., M2 money supply), increased government deficits, and less money flowing into savings can all increase the yield curve, thereby spiking market volatility. In addition, commodity prices affect the yield curve. Generally, decreasing prices steepen the yield curve because they decrease short-term inflation expectations. This pulls the left side of the yield curve downward, making the curve steeper on the whole. In other words, when commodity prices drop, the yield curve steepens, and the VIX should see an increase. But our current market, in which commodity prices are at all-time lows, doesn’t seem to have an increased VIX, which is interesting from a theoretical standpoint. Overall, the picture is complicated: (click to enlarge) Investment Strategies for a Volatile Market For now, we can expect that the yield curve will steepen and prepare our portfolios for such an event. I don’t recommend buying the VXX outright because it’s a garbage imitation of the VIX and will cause you to lose money in the long run. However, a spike in VIX should result in a spike in the VXX, which could leave you with a handful of cash should you have call options on this ETF. But let’s look at some more realistic strategies (I hate the VXX). If volatility increases and you are a risk-averse investor, the easiest “safe” strategy is to exit the market – as reasonably as you can – before increased volatility hits. Of course, most people reading this are likely “buy-and-hold” investors, so such a method might be lost on you. One fundamental idea behind the buy-and-hold strategy is that you don’t want to miss those days with the most significant returns, which tend to happen during days of high market volatility. Of course, if you’re in the market all the time, you’re also gaining exposure to those days with the most significant losses. And a significant loss hurts a lot more than a significant gain. Going from 100 to 80 requires a 20% drop, but going from 80 to 100 requires a 25% gain. The uphill battle is harder. Perhaps the best selling strategy is a staged sale strategy. In this strategy, you sell predetermined chunks of your stocks and either hold cash or reinvest (see below). The staged sell is like the opposite of dollar cost averaging. If you don’t want to worry about market timing but want to liquidate, staged selling is your best bet. Nevertheless, for buy-and-hold investors, volatile markets can be gold mines. An increase in volatility in the general market will not hurt the fundamentals of a company. Thus, a volatile market will allow you access to sporadic dips on stocks with solid fundamentals. This is a good time to buy such stock. However, when buying, realize that some things are different in a volatile market. If you’re not in the habit of buying with limit orders, get into that habit now. Volatile markets move quickly and have high volume; your market order is likely much different from that what you expect. In addition, the bid-ask quotes you’re looking at now might be very different from the real bid-ask quotes. And then there’s increased delays and slippage… This is all general strategy. What about choosing individual stocks during a volatile market? As stated, a volatile market gives you access to a myriad of stocks that hit dips simply as a result of increased volatility on the stock. In the past, such a low would often be explained by the company’s fundamentals. But in a volatile market, the lows that looked large in the past will soon be considered the norm. As a fundamental investor, your best bet is to ignore the daily changes in stock price and instead set a buy limit order that you consider to be “too low.” Set the order as “good for the month” and get your stock at a discount. As for the types of stock to add to your portfolio, choose stock that are relatively safe and undervalued during periods of increased volatility. REITs make good choices. Switching out low-yield dividend stocks for high-yield dividend stocks makes sense, just as switching out growth stocks for value stocks makes sense. Depending on your portfolio, this might be a good time to step back and question the purpose of the portfolio. Are you focused on growth? Passive income via dividends? In the previous case, you should have an existing exit strategy. Perhaps now is the time to take your profits and look to restructure your portfolio with undervalued growth stocks. If your goal is passive income, holding on to your current dividend stocks and REITs makes sense in terms of your overall objective, and you might have no exit strategy at all. But at this time, a day’s worth of research into your current dividend stocks’ fundamentals can give you some clues as to whether dropping the stock for cash (or switching it out for a better option) is the right choice. Overall, for investors, getting defensive as the market has a seizure isn’t the right strategy because you should have been defensive in the first place. But let’s assume you need to get defensive all of the sudden. What are some immediate actions you can take? Switching out common stock for preferred stock is a good choice because preferred stock tends to have lower beta – i.e., it’s less correlated with general market moves. Dropping the beta of your overall portfolio can ensure that your portfolio contains companies that you believe are fundamentally strong and yet will not be hit hard by market corrections. Here’s a general common-to-preferred and visa versa strategy for volatile markets: Switch out common stock for preferred stock when the market appears to be overbought. You’ll have sold common stock at a high, switching them for preferred stock that are more protected against drops. If the market does drop for an extended time, drop the preferred stock, which protected value and brought you dividends, in favor of common stock, which you can now buy at a low. Overall, you want to drop your portfolio’s beta when you believe the volatility is coupled with a downward trend. You should still perform well during the good times at the same time you’re protecting your capital with a low-beta portfolio. The following are some low-beta stocks I recommend: Pfizer (NYSE: PFE ) Wal-Mart (NYSE: WMT ) Avista (NYSE: AVA ) Request a Statistical Study If you would like for me to run a statistical study on a specific aspect of a specific stock, commodity, or market, just request so in the comments section below. Alternatively, send me a message or email.

On Contango-Based XIV Trading Strategies

Summary In July 2014, Seeking Alpha author Nathan Buehler discussed a strategy where you short VXX when VIX goes from backwardation to contango, and cover when VIX re-enters backwardation. Buying XIV rather than shorting VXX is a very similar idea. The XIV version of Mr. Buehler’s strategy can be viewed as making a 1-day bet on XIV whenever VIX is in contango. VIX contango is a useful predictor of 1-day XIV growth. But historically a contango cut-point around 5% rather than 0% generates better raw and risk-adjusted returns. XIV is extremely risky (beta > 4), but trading strategies based on VIX contango appear promising. Background The VelocityShares Daily Inverse VIX Short-Term ETN (NASDAQ: XIV ) has had tremendous growth since it was introduced in late 2010, but has suffered major losses recently. (click to enlarge) The recent 11.9% dip in the SPDR S&P 500 Trust ETF (NYSEARCA: SPY ) coincided with XIV losses of 55.7%. XIV is still ahead of SPY since inception by a fair amount ($26.2k vs. $18.0k), but the extreme volatility of XIV makes it arguably an inferior investment (Sharpe ratio = 0.040 for XIV, 0.055 for SPY). In my view, XIV is a rather dubious fund to buy and hold long-term. It amplifies returns, but seems to amplify volatility even more, resulting in worse risk-adjusted returns than SPY. But trading XIV based on VIX contango – that is, the percent difference between the first and second month VIX futures prices (available at vixcentral.com ) – appears very promising. The purpose of this article is to assess the predictive value of VIX contango, and to assess and attempt to improve a strategy proposed by Seeking Alpha author Nathan Buehler. Data Source and Methods I obtained daily VIX contango/backwardation data and historical XIV and SPY prices from The Intelligent Investor Blog . Daily contango/backwardation is defined as the percent difference between the first and second month VIX futures. While the Intelligent Investor dataset includes simulated XIV data going back to 2004, for this article I only use the actual daily closing prices for XIV since its inception in Nov. 2010. I used R (“quantmod” and “stocks” packages) to analyze data and generate figures for this article. A Look at Nathan Buehler’s Strategy In the Seeking Alpha article Contango and Backwardation Strategy for VIX ETFs , Mr. Buehler suggests shorting VXX when VIX goes from backwardation to contango, and closing the position when VIX re-enters backwardation. The exact time frame for back-testing is a little unclear to me, but Mr. Buehler reported 221.09% total growth from ten VXX trades between May 21, 2012, and April 14, 2014. That is impressive growth. Then again, VXX fell 86.1% over this time period, and XIV gained 213.9%. So it’s a bit unclear how much of the strong performance was due to VXX tanking over the entire time period, and how much was due to the contango strategy providing good entry and exit points. I am not a short seller so I’m more interested in the “buy XIV” version of Mr. Buehler’s strategy. Let’s consider an approach where you look at VIX contango at the end of each trading day. If VIX has entered contango, you buy XIV; if it has entered backwardation, you sell XIV. If we backtest this strategy since XIV’s inception, ignoring trading costs, we get the following performance: (click to enlarge) The contango-based XIV strategy performs well relative to buying and holding XIV for the entire period, achieving a higher final balance ($57.0k vs. $26.2k), smaller maximum drawdown (56.3% vs. 74.4%), and a better Sharpe ratio (0.061 vs. 0.040). Looking at the graph, we see a major divergence in mid-2011 when selling XIV avoided a huge loss. However, there were many times where the contango strategy failed to prevent big losses. Note that buying XIV when VIX enters contango, and selling when it enters backwardation, is equivalent to holding XIV for 1 day whenever VIX is in contango. So this strategy is entirely dependent on VIX contango predicting 1-day XIV growth. VIX Contango and 1-Day XIV Growth For Mr. Buehler’s strategy to have worked so well over the past 5 years, there must have been positive correlation between VIX contango and subsequent 1-day XIV growth. There was indeed some correlation, but not very much. (click to enlarge) The Pearson correlation was 0.059 (p = 0.04), and the Spearman correlation 0.027 (p = 0.35). Note that VIX contango explained only 0.3% of the variability in subsequent 1-day XIV growth. But there does appear to be some predictive value in VIX contango. It’s a little easier to see when you filter out some of the noise and look at mean 1-day XIV growth across quartiles of VIX contango. (click to enlarge) Naturally, we’d hope that VIX contango has enough predictive power to pull the distribution of XIV gains a little bit in our favor. The next figure compares the distribution of XIV gains on days after VIX ended in contango to days after it ended in backwardation. (click to enlarge) The mean was higher for contango vs. backwardation, but the difference was not statistically significant (0.22% vs. -0.26%, t-test p = 0.37). Surprisingly the median was a bit higher for backwardation (0.50% vs. 0.86%, Wilcoxon signed-rank p = 0.62). Towards A Better Cut-Point Holding XIV whenever VIX is in contango is somewhat natural, but there’s no reason we have to use 0% as our cut-point. We might do better if we hold XIV when VIX is in contango of at least 5%, or at least 10%, or some other cut-point. Actually if you look at the regression line in the third figure, you can work out that the expected 1-day XIV growth is only positive for VIX contango of 1.65% or greater. Based on that, we actually wouldn’t want to hold XIV when contango is betwen 0% and 1.65%. Let’s compare 0%, 5%, and 10% VIX contango cut-points. (click to enlarge) The higher cut-point you use, the less frequent your opportunities to trade XIV, but the better the trades tend to be. Notice how the 10% cut-point rarely allows for trades, but tends to climb really nicely when it does. Performance metrics for XIV and the three contango-based XIV strategies are summarized below. Performance metrics for XIV and XIV trading strategies with various VIX contango cut-points. Fund Growth of $10k MDD Overall Sharpe Ratio Sharpe Ratio for Trades XIV $26.2k 74.4% 0.040 0.040 Contango > 0% $57.0k 56.3% 0.061 0.065 Contango > 5% $65.1k 37.3% 0.072 0.090 Contango > 10% $49.3k 14.9% 0.110 0.293 Total growth was best for a contango cut-point of 5%, while maximum drawdown decreased and Sharpe Ratio increased with increasing contango cut-point. (Note that “overall Sharpe ratio” includes the 0% gains on non-trading days, while “Sharpe ratio for trades” does not.) Of course we aren’t restricted to cut-points in 5% intervals here. Let’s play a maximization game and see what VIX contango cut-point would have been optimal for total growth and for overall Sharpe ratio. (click to enlarge) Final balance peaks at VIX contango in the 5-6% range, and is maximized at $100.4k for VIX contango of 5.42%. Overall Sharpe ratio is maximized at 0.115 for VIX contango of 9.95%. Sharpe ratio for trades is maximized at 4.231 for VIX contango at the highest possible value, 21.6%. Of course it wouldn’t make much sense to use a cut-point of 21.6%, as that number is hardly ever reached. Play Both Sides of the Trade? If sufficient VIX contango favors holding XIV, it seems that sufficient VIX backwardation would favor holding VXX. That brings to mind a trading strategy where you buy XIV when VIX contango reaches a certain value, and buy VXX when VIX backwardation reaches a certain value. Trading both XIV and VXX would provide more opportunities for growth. Indeed many of the analyses presented so far are similar when you look at holding VXX based on VIX backwardation. In particular: VIX backwardation is positively correlated with 1-day VXX growth. Regression analysis suggests that VXX on average grows when VIX backwardation is at least 0.38% (equivalently, VIX contango is -0.38% or more negative). Growth of $10k for a backwardation-based VXX strategy is maximized at $13.3k, when you hold VXX when VIX backwardation is at least 5.67%. Unfortunately, 33% growth over 5 years with VXX is nothing compared to 900+% growth with XIV. I experimented with strategies that use both XIV and VXX, but was unable to improve upon XIV-only strategies. Concerns One of my concerns with these strategies is that we’re working with a very weak signal. VIX contango explains about one-third of one percent of XIV’s growth the next day. Contango-based volatility trading strategies do appear to have potential, but keep in mind that VIX contango just isn’t a strong predictor of XIV growth. Another concern is that the excellent historical performance of these strategies may be driven by the bull market of the past 5 years. I think it is very possible that in a bear market these strategies might work poorly for XIV, and perhaps well for VXX. Each strategy involves holding XIV/VXX at certain time intervals, so of course they will be affected by the underlying drift of XIV/VXX. After all, the absolute best you can do with either version of the trade is the total upswing in the fund you are trading over a period of time. Finally, I have noticed in the past that XIV seems to have positive alpha when markets are strong, and negative alpha when markets are weak. This makes it really hard to do portfolio optimization, as the net alpha of a weighted combination of funds including XIV actually depends on what sort of market you’re in. I think an analogous problem could arise for contango-based XIV strategies. For example, holding XIV when VIX contango is at least 5% may only be prudent in periods when XIV itself is rapidly growing, which would typically occur in a strong market. And a strategy that only works during bull markets isn’t very exciting. Conclusions A variant of a strategy discussed by Nathan Buehler, where you hold XIV whenever VIX is in contango, appears promising based on backtested data since Nov. 2010. But increasing the contango cut-point from 0% to 5% increases total returns while also improving Sharpe ratio and reducing MDD. Going to 10% further improves the Sharpe ratio and reduces MDD, but sacrifices total growth as there are fewer trading opportunities. Since Mr. Buehler’s strategy is based on the idea that VIX contango favors XIV, increasing the contango cut-point above 0% makes a lot of sense. It allows us to trade XIV only when we have a substantial advantage due to contango, which reduces trading frequency and therefore trading costs. Strategies based on backtested data are almost always overly optimistic, and I suspect that this analysis is no exception. I am particularly concerned that much of the excellent historical performance is due to XIV’s positive alpha during the past 5 years, which itself was due to a strong market. Therefore, I probably wouldn’t recommend implementing these strategies just yet, at least not with much of your portfolio. Personally, I would consider freeing up a small portion of my portfolio for occasional high-conviction XIV trades based on VIX contango. For example, I might buy XIV on the relatively rare occasion that VIX contango reaches 10%.

Is The SKEW Index Predictive For The S&P 500?

Summary It is difficult to understand exactly what the CBOE Skew Index means, and even more difficult to find a use for it. This has not prevented some commentators from using it as an indicator for the S&P 500, usually in conjunction with the better-known VIX Index. I find no reason to believe that the SKEW Index serves as a useful indicator, and not much logic for thinking that it would. SKEW is useful only to a rather restricted group of professional hedge traders, such as swaps dealers, and can safely be ignored by the rest of us. Given its inexhaustible creativity, it was only a matter of time before the CBOE created an indicator that challenges investors to find a use for it. Meet the SKEW Index ($SKEW:IND). Yet as obscure and difficult to interpret as this index is, there are some who believe it is an indicator for the S&P 500. This article disputes that contention. What is it? The CBOE Skew Index, unveiled in 2011, provides an index of traders’ vertical skew expectations, based on analysis of the volatility smile of deeply-out-of-the-money S&P 500 index options. All of which is jargon, except to option aficionados. But SKEW is just another way of measuring the extent to which investors expect the distribution of security returns to be non-normal. That is, it indicates the degree to which the median return is expected to differ from the mean, and the extent to which the distribution will include more and/or more extreme outliers. On the downside, the latter are known as “black swans” ─ a term I dislike, since it confuses empirical uncertainty with probability (the probability that black swans existed when probability theory was being developed was 100%; uncertainty based on Eurocentric data is a completely separate matter). In option terms, the non-normality of returns means that the assumptions about future volatility embedded in option prices are not symmetrical with respect to strike prices, so that the put and the call at the same strike price do not have the same implied volatility. Thus ─ since most (but by no means all) equity returns are negatively skewed ─ buyers of puts generally assume (and pay for) higher volatility than call buyers. If puts and calls at a given out-of-the-money strike have the same implied volatility, their graphic representation forms a “smile” that indicates that traders assume a normal distribution of returns from the underlying. In most cases, there is a difference between the implied volatility of puts and calls, and the “smile” is more like a smirk: The smirk tells us that option traders do not expect the returns on the underlying to be normally distributed, and in the case shown above, that the outliers will tend to be on the downside. How Has it Behaved? Since the beginning of 2010, the index has developed like this: It requires some explanation. A reading of 100 indicates an expected normal distribution of S&P 500 returns. The higher the reading, the more skewed to the right of the mean traders expect returns to be ─ and the more likely and/or more severe the negative outliers will be. A reading of 100 indicates that the expected probability of a ≥3σ negative outlier is 0.15% (roughly the likelihood of being dealt a full house in five card straight poker with no wild cards), while a reading of 145 indicates a 2.81% expected probability (a bit better than the chance of rolling a double six on a single throw of dice). The trend is disturbing ─ it suggests that traders expect an increasing number of negative outliers, or more damaging ones. It may be that they do, but I suspect that a better explanation is that, since the crash, there has been increased investor interest in “tail insurance,” demand for which is likely to have pushed the index upward. Thus, I believe that the trend does not represent investors’ response to a specific forecast of disaster, but a more widespread realization of the availability and perhaps advisability of insurance. This does not just represent the hedging activity of hedge funds and sophisticated institutions: any product that offers a downside floor, such as the structured notes popular with private bank clients, is hedged in the options market by its issuer. Not surprisingly, such products have become increasingly popular since the crash. What Does It Mean? This is the $64,000 question, because it is not at all clear what the extent to which a tail event might mean, since a tail event, by definition, is something unexpected. ‘Implied volatility’ is a portmanteau term, carrying the freight not contained in the other variables of the Black-Scholes model, all of which are much more precisely defined. It is in effect the bucket into which everything that determines the price of an option ─ other than those narrowly defined variables ─ is placed, including the price markup that options writers demand. This markup varies with market conditions. Put writers may demand higher prices based solely on their perception that they can get them, without reference to volatility forecasts, and purchasers may accommodate them because they are forced by their circumstances (for instance, as issuers of structured products) to hedge, regardless of whether they think the insurance is well priced. To suggest that every change in the volatility smile implies a change in risk perceptions is nonsense. This raises relatively few issues for interpreting the meaning of the VIX Index, because supply and demand for options is significantly determined by perceptions of the identifiable, near-term and “ordinary” risks that the VIX Index measures. But skew is a different matter: there would be no tail events if they were widely anticipated, and even the most extreme possible reading of SKEW implies only a 3% implied probability of one. While changes in demand for out-of-the-money puts is certainly related to fear of tail events, I believe that it is implausible to argue that it can be predictive of them. Much demand for deeply-out-of-the-money puts is inherently “lumpy,” as a new product is launched or a seasoned product’s hedge must be rolled. How Does SKEW Differ from the VIX? The relationship between SKEW and the VIX is an obvious question. The difference was quite significant in the period illustrated here: the linear regression on the VIX trended downward, so they had mildly negative correlation at -0.20, and the VIX was more volatile (σ = 8.0% vs. 2.5%): Over this 6½ year period, the S&P 500’s correlation with the VIX was -0.77, and 0.22 with SKEW, but over shorter periods correlation varied ─ not so dramatically for the VIX, which has a pretty stable correlation with the S&P 500 over time, but very considerably for SKEW: The low correlation between SKEW and the S&P 500, and especially the very substantial variability of the relationship (peak 0.63 and trough -0.17 around the 0.22 average) support my contention that SKEW has little predictive power for the S&P. This should not be so terribly surprising, since the skewness of S&P 500 returns is itself far from stable over time. Comparing this chart with the charts above suggests that SKEW is not even an especially strong indicator for S&P 500 skewness: Note that this chart uses a longer rolling time period. The 90-day results were so volatile as to be virtually unreadable ─ even using 260 data points, the standard error of skewness is 14.9%. The calculation of standard error of skewness is so generous to uncertainty that it constitutes yet another reason to be doubtful of the predictive value of the CBOE Skew Index. There are some other differences between SKEW and the VIX that have attracted comment ─ in particular, when the former spikes, it tends to do so in isolated, one-day spurts, and promptly returns to its earlier level, while the VIX tends to sustain elevated or depressed levels over the course of a week or two. Thus, when SKEW dropped 16 points on October 15 last year, it snapped back completely the next day. In contrast, the VIX spiked upward on the 9th, and did not recover its earlier level until the 23rd. This has been interpreted as the difference between expectation of elevated but still “normal” volatility (